x^4-29x^2=100 solve and show all you work and steps
a=1 b=29 c=100
To solve the equation x^4 - 29x^2 = 100, we can rearrange the equation to have one side equal to zero:
x^4 - 29x^2 - 100 = 0
Now let's solve this quadratic equation using the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
a = 1, b = -29, c = -100
Plugging these values into the quadratic formula, we get:
x = (-(-29) ± √((-29)^2 - 4(1)(-100))) / (2(1))
x = (29 ± √(841 + 400)) / 2
x = (29 ± √1241) / 2
Now we need to simplify the square root of 1241. We notice that 31^2 = 961 is close to 1241, so let's use that as an estimate:
√1241 ≈ √(31^2 * 40)
√1241 ≈ 31√40
Now we can substitute this approximate value of √1241 back into the quadratic formula:
x = (29 ± 31√40) / 2
Now we have two possible solutions for x:
1) x = (29 + 31√40) / 2
2) x = (29 - 31√40) / 2
These are the exact solutions to the equation x^4 - 29x^2 = 100.